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To combat the spread of Covid-19, one(1) roadblock is set on one(1) entrance to a district, to conduct rigorous checking. Both the incoming of vehicles to that entrance, as well as the availability of crew by that entrance at any instant, cannot be predicted and thus are both taken as random. It is only known that the average rate of incoming vehicles is 6 per hour, whereas the average serving capacity of the crew is 9 per hour. Find the following: a) The probability of having less than 5 incoming vehicles in an hour. (3 marks) b) The probability of having at least 8 incoming vehicles in an hour. (4 marks) c) The probability that the next vehicle will arrive within 12 minutes. (3 marks) d) The probability that the next vehicle will arrive later than 17 minutes. (3 marks) e) The probability of having no vehicles in the system (whether in the queue or at the counters). (2 marks) 1) The average number of vehicles waiting in the system. (2 marks) g) The average number of vehicles waiting in the queue. (3 marks) h) The average amount of time a vehicle spends in the system. (2 marks) i) The average amount of time a vehicle spends in the queue. (3 marks) Total : 25 marksi END OF QUESTION PAPER